I'm wondering if can you really make same factor on my own, or Search Engines Like Google does that on their own?

I wish to then add links like here: Screenshot

The search engines do this by itself and all sorts of you should do is to (then) remove a few of the links with the Google Website owner Tools.

They're generally named Site Links and you will google for "Ways to get Site Links Google SERP" and so on - you will find 1000's of strategies for helping Google along.

A obvious navigational structure and internal link structure assistance of course, and consistent anchor texts.

Yes, google will generate that links for you personally.

So far as I understand, Google automagically photos individuals up - there's no direct method to set them. Make certain you've got a proper site map, after which wait I guess.